Abstract
The crack propagation simulation is still an open problem in the mechanical simulation field. In the present work this problem is analyzed using a version of truss-like Discrete Element Method, that here we called DEM. This method has been used with success in several applications in solid mechanical problems where the simulation of fracture and fragmentation is relevant. The formulation of DEM explaining the way the process of rupture could be simulated in consistent form is showed. Also are described details about how the dynamical fracto-mechanical stress intensity factors are computed. The main aim of this paper is to show the ability of this method in simulating fracture and crack propagation in solids, for this, three examples with different levels of complexity are analyzed. The obtained results are presented in terms of the variation of dynamic stress intensity factor in the fracture process, the stress map and geometric configuration on different steps in the simulation of the fracture process, the crack speed and the energetic balance during all the process. These results are compared with experimental and numerical results obtained by other researchers and published in recognized scientific papers. Final commentaries about the performance of the version of lattice model considered are carried out.
Similar content being viewed by others
References
Abraham FF, Brodbeck D, Rudge WE, Xu X (1997) A molecular dynamics investigation of rapid fracture mecahnics. J Mech Phys Solids 45: 1595–1619
Agwai A, Guven I, Madenci E (2011) Predicting crack propagation with peridynamics: a comparative study. Int J Fract 171(1): 65–78
Aliabadi MH, Rooke DP (1991) Numerical fracture mechanics. Computacional Mechanics Publicactions and Kluwer, Southampton
Aliabadi MH, Saleh AL (2002) Fracture mechanics analysis of cracking in plain and reinforced concrete using the boundary element method. Eng Fract Mech 69: 267–280
Anderson TL (2005) Fracture mechanics. fundamentals and applications. CRC Press, Boca Ratón
Barrios D’Ambra RL, Iturrioz I, Coceres H, Kosteski L, Tech TW, Cisilino A (2007) Cálculo del factor de intensidad de tensiones utilizando el método de los elementos discretos. Revista Sul-Americana de Engenharia Estrutural 4: 7–20
Bathe KJ (1996) Finite element procedures. Prentice-Hall, New Jersey
Batra RC, Ching HK (2002) Analysis of elastodynamic deformations near a crack/notch tip by the Meshless Local Petrov-Galerkin (MLPG) method. Comput Model Eng Sci 3: 717–730
Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 37: 229–256
Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free Galerkin methods. Eng Fract Mech 51: 295–315
Belytschko T, Chen H, Xu J, Zi G (2003) Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int J Numer Methods Eng 58: 1873–1905
Brara A, Camborde F, Klepaczko JR, Mariotti C (2001) Experimental and numerical study of concrete at high strain rates in tension. Mech Mater 33: 33–45
Chiaia B, Vervuurt A, Van Mier JG (1997) Lattice model evaluation of progressive failure in disordered particle composites. Eng Fract Mech 57(2/3): 301–318
Cundall PA, Hart RD (1989) Numerical modelling of discontinua. Proc 1st US Conf Discrete Element Methods (Golden, CO), pp 1–17
Dalguer LA, Irikura K, Riera JD, Chiu HC (2001) The importance of the dynamic source effects on strong ground motion during the 1999 Chi-Chi, Taiwan, earthquake: brief interpretation of the damage distribution on buildings. Bull Seismol Soc Am 91/5: 1112–1127
Das BM (1982) Principles of soil dynamics. El Paso, Texas
Falk ML, Needleman A, Rice JR (2001) A critical evaluation of dynamic fracture simulations using cohesive surfaces. J Phys IV 11: 43–52
Freund LB (1998) Dynamic fracture mechanics. Cambridge University Press, Cambridge
Furuya Y, Noguchi H (1998) A combined method of molecular dynamics with micromechanics improved by moving the molecular dynamics region successively in the simulation of elastic–plastic crack propagation. Int J Fract 94: 17–31
Gao H (1996) A theory of local limiting speed in dynamic fracture. J Mech Phys Solids 44: 1453–1474
Guo YJ, Nairn JA (2004) Calculation of J-integral and stress intensity factors using the material point method. Comput Model Eng Sci 6: 295–308
Ha YD, Bobaru F (2011) Characteristics of dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78(6): 1156–1168
Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1): 229–244
Huespe AE, Oliver J, Sanchez PJ, Blanco S, Sonzogni V (2006) Strong discontinuity approach in dynamic fracture simulations. Mecánica Computacional 24: 1997–2018
Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24: 361–364
Iturrioz I, Miguel LFF, Riera JD (2009) Dynamic fracture analysis of concrete or rock plates by means of the discrete element method. Lat Am J Solids Struct 6: 229–245
Kalthoff JF, Winkler S (1987) Failure mode transition at high rates of shear loading. Int Conf Impact Load Dyn Behav Mater 1: 185–195
Kosteski L, Barrios R, Iturrioz I. (2008) Determinación de parámetros fractomecánicos estáticos y dinámicos utilizando el método de los elementos discretos compuestos por barras. Revista Internacional Métodos numéricos para cálculo y diseño en ingeniería, Cimne 24: 323–343
Kosteski L, Barrios R, Iturrioz I. (2009) Fractomechanics parameter calculus using the discrete element method with bars. Lat Am J Solids Struct 6: 301–321
Kosteski L, Iturrioz I, Batista RG, Cisilino AP (2011) The truss-like discrete element method in fracture and damage mechanics. Eng Comput 28: 6–765787
Kupfer HB, Gerstle KH (1973) Behaviour of concrete under biaxial stresses. J Eng Mech Div Am Soc Civ Eng 99: 853–866
Miguel LFF, Riera JD, Iturrioz I (2008) Influence of size on the constitutive equations of concrete or rock dowels. Int J Numer Anal Methods Geomech 32/15: 1857–1881
Miguel LFF, Iturrioz I, Riera JD (2010) Size effects and mesh independence in dynamic fracture analysis of brittle materials. Comput Methods Model Eng Sci 56: 1–16
Munjiza A, Bangash T, John NWM (2004) The combined finite-discrete element method for structura failure and collapse. Eng Fract Mech 71: 469–483
Munjiza A (2009) Special issue on the discrete element method: aspects of recent developments in computational mechanics of discontinua. Eng Comput 26(6) http://www.emeraldinsight.com/journals.htm?articleid=1806113&show=html
Murphy N, Ali M, Ivankovic A (2006) Dynamic crack bifurcation in PMMA. Eng Fract Mech 73: 2569–2587
Nayfeh AH, Hefzy MS (1978) Continuum modeling of three-dimensional truss-like space structures. AIAA J 16/8: 779–787
Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54: 525–531
Nishioka T (1998) On the dynamic J Integral in dynamic fracture mechanics. In: Cherepanov GP (eds) FRACTURE: a topical encyclopedia of current knowledge dedicated to alan arnold grith. Krieger Publishing Company, Malabar, pp 575– 617
Oliver J, Huespe AE, Pulido MGD, Chaves E (2001) From continuum mechanics to fracture mechanics: the strong discontinuity approach. Eng Fract Mech 69: 113–136
Rabczuk T, Belytschko T (2004) Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Methods Eng 61(13): 2316–2343
Rabczuk T, Belytschko T (2007) A three dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29-30): 2777–2799
Rabczuk T, Bordas S, Zi G (2007) A three-dimensional meshfree method for continuous multiplecrack initiation, nucleation and propagation in statics and dynamics. Comput Mech 40(3): 473–495
Rabczuk T, Song JH, Belytschko T (2009) Simulations of instability in dynamic fracture by the cracking particles method. Eng Fract Mech 76: 730–741
Rashid MM (1998) The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis. Comput Methods Appl Mech Eng 154: 133–150
Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture—I. Crack initiation and crack arrest. Int J Fract 25: 247–262
Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture – II. Microstructural aspects. Int J Fract 26: 65–80
Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture – III. Steady state crack propagation and crack branching. Int J Fract 26: 141–154
Ravi-Chandar K, Knauss WG (1984) An experimental investigation into dynamic fracture – IV. On the interaction of stress waves with propagating cracks. Int J Fract 26: 189–200
Remmers JJC, Borst R, Needleman A (2008) The simulation of dynamic crack propagation using the cohesive segments method. J Mech Phys Solids 56: 70–92
Riera JD (1984) Local effects in impact problems on concrete structures. In: Proceedings, conference on structural analysis and design of nuclear power plants, vol 3. Porto Alegre, RS, Brasil, CDU 264.04:621.311.2:621.039
Riera JD, Iturrioz I (1995) Discrete element dynamic response of elastoplastic shells subjected to impulsive loading. Commun Numer Methods Eng 11: 417–426
Riera JD, Iturrioz I (1998) Discrete element model for evaluating impact and impulsive response of reinforced concrete plates and shells subjected to impulsive loading. Nucl Eng Des 179: 135–144
Riera JD, Rocha MM (1991) A note on the velocity of crack propagation in tensile fracture. Revista Brasileira de Ciencias Mecânicas 12/3: 217–240
Rinaldi A, Lai YC (2007) Statistical damage theory of 2D lattices: Energetics and physical foundations of damage parameter. Int J Plast 23: 1769–1825
Rinaldi A, Krajcinovic D, Peralta P, Lai YC (2008) Lattice models of polycrystalline microstructures: A quantitative approach. Mech Mater 40: 17–36
Rios RD, Riera JD (2004) Size effects in the analysis of reinforced concrete structures. Eng Struct 26: 1115–1125
Rocha MM, Riera JD, Krutzik NJ (1991) Extension of a model that aptly describes fracture of plain concrete to the impact analysis of reinforced concrete. In: International conference on structural mechanics reactor technology (SMIRT 11) Tokyo, Japan
Schnaid F, Spinelli L, Iturrioz I, Rocha M (2004) Fracture mechanics in ground improvement design. Ground Improv UK 8: 7–15
Sigmund O (1994) Materials with prescribed constitutive parameters: An inverse homogenization problem. Int J Solids Struct 31/17: 2313–2329
Tabiei A, Wu J (2003) Development of the DYNA3D simulation code with automated fracture procedure for brick elements. Int J Numer Methods Eng 57: 1979–2006
Williams ML (1957) On the stress distributions at the base of a stationary crack. J Appl Mech 24: 109–114
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kosteski, L., Barrios D’Ambra, R. & Iturrioz, I. Crack propagation in elastic solids using the truss-like discrete element method. Int J Fract 174, 139–161 (2012). https://doi.org/10.1007/s10704-012-9684-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-012-9684-4